A Joint Decoding and Equalization Algorithm for Increased Efficiency and Lowered Complexity in Digital Communication Systems


Reduce signal distortion and system complexity and increase computational efficiency in digital communications systems with an algorithm that combines the equalization and decoding tasks into one process.


The greatest challenge facing digital communications is the ability to accurately transfer information faster. When dealing with sub-optimal communication channels, digital signals are subject to significant signal degradation (through dispersion and noise) and are often laden with errors. While receiver based equalizers often compensate for dispersion errors, most systems also require additional corrective steps. The addition of a forward error correction step can often help compensate for the limits of equalization, but this requires an additional computation at the receiver which slows the flow of information. This algorithm combines the equalization and error correction coding, used in all digital communication systems, into one process with very low complexity. Combining these two steps results in greater computational efficiency and reduces overall complexity allowing for more efficient Soft-Input, Soft-Output (SISO) transfers. While the concept of joint equalization is well-known, implementations are often highly complicated. Traditional techniques require an exponential increase in complexity to recover from dispersion or signal smearing (2x complexity, where x is the number of periods of smearing).

This method scales linearly with complexity (2x complexity, where x is the number of periods of smearing), leading to a drastic reduction in complexity for error prone applications. In addition to the decrease in complexity, the combination of equalization and error correction utilize computational resources more efficiently. Computational efficiency lowers the total costs associated with digital signal reconstruction in all applications. Specifically this invention uses a Minimum Mean Squared Error (MMSE) equalizer which receives and outputs soft information, i.e. it is a soft-input soft-output (SISO) equalizer. This soft information is exchanged with a SISO decoder, opportune for error correction decoders. The nature of the equalizer permits solutions beyond one-dimensional data streams and for both channels of arbitrary length and for signal constellations of arbitrary size. A SISO MMSE-based iterative equalizer/decoder has been tested for one- and two-dimensional data recording systems, has been successfully tested on real data for wireless communications links, and can be applied to any digital communication system to enhance the speed and accuracy of information transfer.


  • Wireless Communications: Cellular Phones, Base Stations
  • Wireline Communications: ADSL/VDSL/xDSL Modems, Backplane interconnects, Optical links with dispersion compensation
  • Data Storage: Optical Storage, Magnetic Storage
  • Cable Systems: Television, Broadband Digital Microwave Communications: Digital Radio-Relay Links


  • Low Complexity: Where multi-step equalization and decoding systems tend to scale exponentially, this single step system combines the equalization and decoding tasks into one process allowing it to scale linearly, resulting in less complexity for large systems.
  • Efficient: Offers greater performance than systems that have separate equalization and decoding steps without sacrificing cost and complexity.
  • Cost Effective: Implementation is low-cost.
  • Flexible: Can be used in a wide variety of digital communication systems.